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Asymptotics for large time of solutions to nonlinear system associated with the penetration of a magnetic field into a substance. (English) Zbl 1224.35189
Summary: The nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is considered. The asymptotic behavior as \(t\to \infty \) of solutions for two initial-boundary value problems are studied. The problem with non-zero conditions on one side of the lateral boundary is discussed. The problem with homogeneous boundary conditions is also studied. The rates of convergence are given. Results presented show the difference between stabilization characters of solutions of these two cases.

MSC:
35K55 Nonlinear parabolic equations
45K05 Integro-partial differential equations
74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
78A30 Electro- and magnetostatics
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